Dynamics of the exact soliton solution of the integrable perturbation of the KdV equation for the field . (a) 1-soliton with the usual localized form but with an unusual deceleration, reflected in the bending of soliton trajectory in the -plane. (b) 2-soliton with the usual elastic scattering and phase shift, but with the dynamics dominated by an unusual accelerated motion.
Exact accelerated soliton in the -plane for the integrable perturbed mKdV equation.
Exact soliton solutions for the integrable perturbation of the SG equation. (a) Accelerating kink solution for . (b) Perturbation in the solitonic form with nontrivial time-dependent asymptotic .
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